I see a lot of things horse owners do that makes me cringe, but unless my advice is asked for I don't give it. I also dislike when outsiders give commands to any animal I am working with. It confuses the poor creature. My family does this a lot with the dogs, and it is very frustrating.
You look like you are in your 20s in your pictures of you and your horse (beautiful mare, by the way). I am a bit surprised that the girl was not intimidated by your age and actually came up and tried to tell you what to do. When I was a teen, I did like telling those younger than me what to do but was intimidated by anyone older. Hence I always listened to those who were older me, and only found out later that their instruction/advice was wrong.
If possible, I try not to allow a horse to go tearing off into a canter or gallop immediately and get them to warm up first. Other than that, really no rules. :)
"You can do something wrong for thirty years and call yourself experienced, you can do something right for a week and experience more than someone who spent thirty years doing the wrong thing." ~WhattaTroublemaker